lazily 0.31.1

A library for lazy evaluation with context caching

lazily

Lazy reactive primitives for Python — Slots, Cells, and Signals with automatic dependency tracking and cache invalidation, plus the language-agnostic lazily-spec wire protocol for mirroring graph state across processes and languages.

Overview

lazily provides a small reactive family for context-aware computation:

• Slot — a lazily-computed cached value that automatically tracks its dependencies (slot / slot_def).
• Cell — a mutable value that invalidates dependent Slots when it changes (cell / cell_def, Cell, CellSlot).
• Signal — an eager derived value that recomputes the instant a dependency invalidates, with no intermediate unset value (signal / signal_def).

Values are lazy by default: dependents are marked dirty on invalidation but only recompute when accessed. When you need eager push-style semantics — recompute immediately, observe v1 → v2 with no unset window — reach for Signal, which layers a puller over a memoized Slot. The Slot → Cell → Signal progression lets you choose lazy or eager per derived value within one graph. An equal recompute is suppressed by a PartialEq/memo guard, so unchanged values never cascade downstream work.

There is no dedicated Context class — a plain dict is the context. Slots use themselves as dictionary keys to cache values, so any dict works as the reactive "world."

Feature coverage

The full lazily capability set across every binding. Legend: ✅ shipped · ~ partial · — absent or not applicable. The canonical matrix with per-cell notes and platform carve-outs lives in lazily-spec § Cross-Language Coverage.

Feature	Rust	Python	Kotlin	JS	Dart	Zig	Go	C++
Reactive graph — core Cell / Slot / Effect (+ derived Signal = Slot.eager) / memo / batch	✅	✅	✅	✅	✅	✅	✅	✅
Keyed-map materialization (SlotMap) — mint-on-access derived slots: transparency + deferral (#lzmatmode)	✅	✅	✅	✅	✅	✅	✅	✅
Thread-safe keyed map (ThreadSafeSlotMap) — Send + Sync + materialization confluence (#lzmatmode)	✅	✅	✅	✅	✅	✅	✅	✅
Async keyed map (AsyncSlotMap) — eventual transparency (#lzmatmode)	✅	✅	✅	✅	✅	✅	✅	✅
Keyed-map sync — membership propagation + materialize-on-ingest + derived-aggregate transparency (#lzfamilysync)	✅	✅	✅	✅	✅	✅	✅	✅
Thread-safe context (lock-backed)	✅	✅	✅	✅	✅	✅	✅	✅
Async reactive context	✅	✅	✅	✅	✅	✅	✅	✅
Flat state machine	✅	✅	✅	✅	✅	✅	✅	✅
Harel state charts	✅	✅	✅	✅	✅	✅	✅	✅
Keyed reactive maps (ReactiveMap: CellMap / SlotMap) + CellTree + reconcile	✅	✅	✅	✅	✅	✅	✅	✅
Memoized semantic tree (SemTree)	✅	✅	✅	✅	✅	✅	✅	✅
Stable-id alignment (manufactured identity)	✅	✅	✅	✅	✅	✅	✅	✅
Reactive queue (QueueCell SPSC/MPSC + QueueStorage adapter)	✅	✅	✅	✅	✅	✅	✅	✅
Broadcast topic (TopicCell) — independent cursors + durable replay + safe GC (#lztopiccell)	✅	✅	✅	✅	✅	✅	✅	✅
Competing-consumer work queue (WorkQueueCell) — exclusive leases + ack/nack + redelivery + DLQ (#lzworkqueue)	✅	✅	✅	✅	✅	✅	✅	✅
Merge algebra + MergeCell — associative MergePolicy (KeepLatest/Sum/Max/SetUnion/RawFifo), Cell ≡ MergeCell<KeepLatest>, Reactive/Source split (#relaycell)	✅	✅	✅	✅	✅	✅	✅	✅
RelayCell — conflating relay + BackpressurePolicy + SpillStore + Transport + Inbox/Outbox + Rate/Window/Expiry/Priority/keyed policies (#relaycell)	✅	✅	✅	✅	✅	✅	✅	✅
Free-text character CRDT (TextCrdt)	✅	✅	✅	✅	✅	✅	✅	✅
TextCrdt delta sync (version_vector / delta_since / apply_delta)	✅	✅	✅	✅	✅	✅	✅	✅
CrdtTree lossless document contract (#lzcrdttree)	✅	✅	✅	✅	✅	✅	✅	✅
Move-aware sequence CRDT (SeqCrdt)	✅	✅	✅	✅	✅	✅	✅	✅
Lossless tree CRDT core (LosslessTreeCrdt, M1)	✅	✅	✅	✅	✅	✅	✅	✅
Lossless tree — dotted-frontier anti-entropy	✅	✅	✅	✅	✅	✅	✅	✅
Lossless tree — concurrent merge convergence	✅	✅	✅	✅	✅	✅	✅	✅
Registers (LWW / MV) + PnCounter + CellCrdt	✅	✅	✅	✅	✅	✅	✅	✅
IPC wire — Snapshot + Delta + CrdtSync	✅	✅	✅	✅	✅	✅	✅	✅
Shared-memory blob path (ShmBlobArena)	✅	✅	✅	✅	✅	✅	✅	✅
Cross-process zero-copy transport (BlobBackend / shm / arrow)	✅	✅	✅	✅	✅	✅	✅	✅
Distributed CRDT plane (CrdtPlaneRuntime / anti-entropy)	✅	✅	✅	✅	✅	✅	✅	✅
Reliable sync — resync coordinator + at-least-once durable outbox + OR-set/LWW liveness (#lzsync)	✅	✅	✅	✅	✅	✅	✅	✅
Storage-independent durable outbox (OutboxStore + shared outbox protocol; SQLite/Room/IndexedDB/file adapters)	✅	✅	✅	✅	✅	✅	✅	✅
Reliable-sync transport seam + full-duplex SyncDriver loop (IpcSink/IpcSource, #sync-driver)	✅	✅	✅	✅	✅	✅	✅	✅
Distributed plane — WebRTC transport + signaling	✅	✅	✅	✅	✅	✅	✅	✅
State projection / mirror	✅	✅	✅	✅	✅	✅	✅	✅
Causal receipts (CausalReceipts outcome projection)	✅	✅	✅	✅	✅	✅	✅	✅
Message-passing + RPC command plane (command-plane-v1)	✅	✅	✅	✅	✅	✅	✅	✅
C-ABI FFI boundary	✅	✅	✅	✅	✅	✅	✅	✅
Permission boundary (PeerPermissions / RemoteOp)	✅	✅	✅	✅	✅	✅	✅	✅
Capability negotiation (SessionHandshake)	✅	✅	✅	✅	✅	✅	✅	✅
Instrumentation / benchmarks	✅	✅	✅	✅	✅	✅	✅	✅
Temporal sources — TimerCell / IntervalCell / CronCell / DeadlineCell over a logical clock (#lztime)	✅	✅	✅	✅	✅	✅	✅	✅
Rate-shaping operators — DebounceCell / ThrottleCell / SampleCell / ProbabilisticSampleCell (#lzrateshape)	✅	✅	✅	✅	✅	✅	✅	✅
Membership + failure detection — MembershipCell (SWIM + Phi-accrual) / PeerSet / PeerChangeEvent (#lzmemb)	✅	✅	✅	✅	✅	✅	✅	✅
Distributed coordination — LeaseCell / LeaderCell / LockCell / SemaphoreCell / BarrierCell+QuorumCell (#lzcoord)	✅	✅	✅	✅	✅	✅	✅	✅
Presence + ephemeral plane — PresenceCell / AwarenessCell / EphemeralCell + Ephemeral/Durable markers (#lzpresence)	✅	✅	✅	✅	✅	✅	✅	✅
Stream windowing — TumblingWindow / SlidingWindow / SessionWindow over the merge algebra (#lzwindow)	✅	✅	✅	✅	✅	✅	✅	✅
Fault tolerance — CircuitBreakerCell / RetryPolicyCell / BulkheadCell / TimeoutCell (#lzresilience)	✅	✅	✅	✅	✅	✅	✅	✅
Embedded-service plane — HealthCell / ReadinessCell / DiscoveryCell / ServiceRegistry (#lzservice)	✅	✅	✅	✅	✅	✅	✅	✅

Installation

pip install lazily

Example usage

from lazily import CellSlot, cell, slot

# Cells hold a value that can be updated.
name = CellSlot[dict, dict, str]()


# Slots are functions that depend on cells and other slots.
@slot
def greeting(ctx: dict) -> str:
    print("Calculating greeting...")
    return f"Hello, {name(ctx).value}!"


# A CellSlot can also have a default value.
@cell
def response(ctx: dict) -> str:
    return "How are you?"


@slot
def greeting_and_response(ctx: dict) -> str:
    print("Calculating greeting_and_response...")
    return f"{greeting(ctx)} {response(ctx).value}"


ctx = {}

name(ctx).value = "World"

# First access: runs the function
print(greeting(ctx))
# Calculating greeting...
# 'Hello, World!'

# Second access: uses cache (no print)
print(greeting(ctx))
# 'Hello, World!'

# Dependencies also access cached values
print(greeting_and_response(ctx))
# Calculating greeting_and_response...
# 'Hello, World! How are you?'

# Dependencies also cached
print(greeting_and_response(ctx))
# 'Hello, World! How are you?'

# Update cell: invalidates cache
name(ctx).value = "Lazily"

# Access again: re-runs the function
print(greeting_and_response(ctx))
# Calculating greeting_and_response...
# Calculating greeting...
# 'Hello, Lazily! How are you?'

# Another access: uses cache
print(greeting_and_response(ctx))
# 'Hello, Lazily! How are you?'

Core Concepts

Context

A plain dict is the context. It owns all cached Slot values; Slots store their cache under themselves as keys. The current implementation is single-threaded — create one dict per reactive graph.

Slot

A Slot wraps a compute function (ctx) -> T; the result is cached after first access. Dependencies are discovered automatically via a global slot_stack — any Slot or Cell read during computation becomes a dependency and re-subscribes on every recompute, so conditional branches update the dependency graph with no manual cleanup. When a dependency invalidates, the Slot only marks its cache dirty; it does not recompute until called again.

Type	Purpose
BaseSlot[C_in, C_ctx, T]	Base slot without subscriber support
Slot[C_in, C_ctx, T]	Slot with dependency tracking and invalidation
slot	Decorator: Slot with an identity context resolver
slot_def(resolve_ctx)	Decorator factory for a custom context resolver

Cell

A Cell holds a mutable value. Reading cell.value inside a Slot auto-subscribes that Slot; assigning cell.value = x (or cell.set(x)) compares old and new via != and, only if changed, cascades invalidation to dependents.

Type	Purpose
Cell[T]	Mutable value with subscription support
CellSlot[C_in, C_ctx, T]	Slot that returns a Cell
cell	Decorator: CellSlot with an identity resolver
cell_def(resolve_ctx)	Decorator factory for a custom context resolver

Signal

A Signal is the eager counterpart to a lazy Slot — one step further along the Slot → Cell → Signal progression. Where a Slot marks itself dirty on invalidation and recomputes on the next read, a Signal recomputes the instant a dependency is invalidated, before the mutating call returns. The value is always materialized, so observers never see an intermediate unset value.

from lazily import CellSlot, signal

n = CellSlot[dict, dict, int]()


@signal
def doubled(ctx: dict) -> int:
    return n(ctx).value * 2


ctx: dict = {}
n(ctx).value = 1

s = doubled(ctx)   # eager: materialized now
print(s.value)     # 2

n(ctx).value = 5   # doubled recomputes immediately
print(s.value)     # 10 — already current, no lazy read needed

A Signal is composed from existing primitives, not a parallel engine: a memoized Slot supplies glitch-free, memo-guarded recomputation, and a small puller re-materializes it after every invalidation to supply the eagerness. Consequently a Signal inherits the memo guard (an equal recompute suppresses the downstream cascade). signal.dispose() removes the eager puller — the value stays readable but reverts to lazy (recompute-on-read) behavior.

Type	Purpose
Signal[T]	Eager derived value bound to a single context
signal	Decorator: context-cached eager-Signal factory (one Signal per context)
signal_def(resolve_ctx)	Decorator factory with a custom context resolver

StateMachine

StateMachine[S, E] is a finite state machine backed by a reactive Cell, so its state participates in dependency tracking like any other reactive value. Construct it with StateMachine(ctx, initial, transition) where transition is a pure (state, event) -> next_state | None (returning None rejects the event). send(event) returns whether the transition was accepted; a self-transition to an equal state is accepted but suppressed by the Cell's PartialEq guard.

Reactive collections, async, and thread-safe contexts

lazily-py also implements the lazily-spec compute-layer MUSTs, each ported from its Lean formal model in lazily-formal:

• ReactiveMap / CellMap / SlotMap / CellTree — keyed reactive collections (#reactivemap) with independent value/membership/order signals and atomic move. One generic ReactiveMap over a handle kind; CellMap (input cells, adds set + eager entry) and SlotMap (derived slots, lazy get_or_insert_with + eager materialize_all) are its specializations.
• QueueCell — a reactive FIFO queue (SPSC primitive with an MPSC-via-batch usage rule) with a pluggable QueueStorage backend. Reader-kind invalidation (head/len/is_empty/is_full/closed), bounded reactive backpressure via is_full, and the closure lifecycle (drain / Closed-distinct-from-Empty / idempotent).
• reconcile_ops — move-minimized keyed reconciliation (LIS kernel).
• AsyncSlot / AsyncEffect — the async slot lifecycle with stale-completion discard, and cleanup-before-body effect scheduling.
• ThreadSafeContext — a lock-serialized batch boundary that coalesces writes into one invalidation pass.
• lazily.ffi — the C-ABI FFI boundary (LazilyFfiStatus, LazilyFfiMessageKind incl. CrdtSync = 3, LazilyFfiBytes).

The test suite gates on lazily-formal's lake build (every theorem checks) and mirrors the named Lean theorems as property tests. See SPEC.md for the full compliance surface.

Reactive queue — lazily.queue

QueueCell is a FIFO collection composed of reactive cells — not a new cell kind — that adds queue semantics (push to tail, pop from head) to the reactive graph. It is an SPSC primitive; MPSC is a usage rule on the same primitive — multiple producers push inside one batch, which serializes the pushes into a deterministic order. The reactive shell wraps a pluggable QueueStorage backend (default VecDequeStorage); the shell owns the reader-kind version cells and invalidates by reader kind — a push to a non-empty queue does NOT invalidate the head reader, a pop does.

from lazily import QueueCell, QueuePopError, batch

ctx = {}
q: QueueCell[str] = QueueCell(ctx)

q.try_push("a")
q.try_push("b")
assert q.head() == "a"
assert q.len() == 2
assert q.try_pop() == "a"

# Bounded queue → reactive backpressure via is_full.
bq = QueueCell[int].with_capacity(ctx, 2)
bq.try_push(1)
bq.try_push(2)
assert bq.is_full()
assert bq.try_push(3).label == "Full"   # reject at capacity
assert bq.try_pop() == 1
assert not bq.is_full()                  # pop freed a slot → is_full reader invalidated

# MPSC: multiple producers push inside one batch → one invalidation pass.
batch(lambda: (q.try_push("p1"), q.try_push("p2")))

# Closure: pop on closed+empty returns Closed (distinct from Empty).
q.close()
assert q.is_closed()
assert q.try_push("x").label == "Closed"

Competing-consumer work queue

WorkQueueCell provides exclusive FIFO claims with visibility deadlines, worker-scoped acknowledgements, tail retries, and bounded dead-letter handling. Item ids survive retries while each claim gets a fresh delivery id.

from lazily import WorkQueueCell

work = WorkQueueCell[str](ctx, visibility_timeout=10, max_deliveries=3)
work.push("job")
delivery = work.claim("worker-a", 100)
assert delivery is not None
assert work.ack("worker-a", delivery.delivery_id)

The reader-kind independence law (a push to a non-empty queue does not change head, so the head reader is not invalidated) comes for free from the Cell != (PartialEq) guard: after each op the shell re-derives each reader-kind cell from storage and writes it back, and a cell whose value did not change is not invalidated.

IPC — the lazily-spec wire protocol

lazily.ipc implements the language-agnostic lazily-spec wire protocol, so a Python graph's state can be mirrored to remote observers across processes and languages. The JSON encoding is byte-compatible with the Rust (lazily-rs), Zig (lazily-zig), and TypeScript (@lazily/signaling) bindings, and is validated against the canonical lazily-spec/conformance fixtures (vendored under tests/conformance/).

Two message kinds flow over any transport (WebSocket text, WebRTC data, FFI buffer):

• Snapshot — the full graph state at an epoch (nodes, edges, roots).
• Delta — an ordered batch of the 7 DeltaOp variants (CellSet, SlotValue, Invalidate, NodeAdd, NodeRemove, EdgeAdd, EdgeRemove) applied with epoch sequencing and fail-closed resync.

from lazily import (
    Snapshot, NodeSnapshot, EdgeSnapshot, ShmBlobRef,
    Delta, DeltaOp, IpcMessage,
)

# Build and serialize a snapshot — encode_json() returns transport-agnostic bytes.
snap = Snapshot(
    epoch=7,
    nodes=[
        NodeSnapshot.payload(1, "i32", bytes([1, 2, 3])),
        NodeSnapshot.opaque(2, "opaque-type"),
        NodeSnapshot.shared_blob(3, "text/plain", ShmBlobRef(0, 16, 1, 7, 999)),
    ],
    edges=[EdgeSnapshot(2, 1), EdgeSnapshot(3, 1)],
    roots=[1, 2],
)
wire = IpcMessage.of_snapshot(snap).encode_json()
assert IpcMessage.decode_json(wire).snapshot == snap

# An incremental delta carrying mutations.
delta = Delta.next(40, [
    DeltaOp.cell_set(1, bytes([10])),
    DeltaOp.invalidate(3),
])
IpcMessage.of_delta(delta).encode_json()

A PeerPermissions boundary gates what is shared: it is default-deny, so only nodes a peer is explicitly allowed to read are serialized into a snapshot or delta — non-allowlisted nodes are omitted entirely.

Shared-memory blobs — ShmBlobArena

ShmBlobArena lets a Python process host blob payloads (not just carry ShmBlobRef descriptors). It is a bytearray-backed, append-only arena with a 40-byte header (LZSH magic + FNV-1a-64 checksum) and wraparound, ported from the lazily-rs ShmBlobArena<B> and byte-compatible with the Rust and Zig arenas. The module exports ShmBlobArena, ShmBlobArenaError (with its variant subclasses), and SHM_BLOB_HEADER_LEN.

Lossless tree CRDT — lazily.lossless_tree_crdt

LosslessTreeCrdt (#lzlosstree) is a single rooted concrete-syntax tree whose leaves own every rendered byte — render(tree) == source_text for valid, invalid, and unknown source alike. Where TextCrdt is a flat lossless floor, this is the structured tree that can itself be the wire authority. Element nodes own structure only; all text lives in leaf nodes tagged Token / Trivia / Raw / Error, so unknown/invalid spans round-trip exactly as Raw/Error leaves rather than being discarded.

from lazily import LeafKind, LosslessTreeCrdt, SeedElement, SeedLeaf
from lazily.lossless_tree_crdt import ROOT

tree = LosslessTreeCrdt(peer=1)
heading = tree.create_node(ROOT, None, SeedElement("heading"))
tree.create_node(heading, None, SeedLeaf(LeafKind.TOKEN, "# "))
title = tree.create_node(heading, None, SeedLeaf(LeafKind.RAW, "Título"))
assert tree.render() == "# Título"

# Op-based delta sync: fork, diverge, converge through a dotted frontier.
other = tree.fork(peer=2)
other.edit_leaf(title, 0, 0, "X")
tree.apply_update(other.diff(tree.frontier()))
assert tree.render() == other.render()

Leaf text embeds TextCrdt wholesale; child order is a fractional index (key_between); the clock is a Lamport TreeOpId. Anti-entropy is op-based over a dotted, non-contiguous version frontier (TreeVersionFrontier) — a dot set (contiguous prefix + sparse holes), never a per-peer max, so a missing interior op stays representable and re-requestable. Leaf-local wire offsets are UTF-8 bytes (byte_to_char). The wire codec (tree_update_to_wire / tree_update_from_wire) validates against lazily-spec's lossless-tree-delta.json, and all nine conformance/lossless-tree/ fixtures replay.

Command / RPC message plane — lazily.command

command-plane-v1 is an additive sibling to Snapshot / Delta / CrdtSync: four evented frames (CommandSubmit / CommandCancel / CommandEvents / CommandProjection) that carry command traffic, not cell state. lazily owns the envelope; the namespace owns the IpcValue payload, which lazily never decodes.

The single hard rule: terminal authority is the causal receipt. A command is terminal only when a terminal CausalReceipt for its command_id folds in (applied, or rejected — including the cancelled / superseded / timed_out reasons). observed / accepted / started events are progress only; a transport ACK is never terminal.

from lazily import (
    CommandPolicy, CommandRpcClient, CommandSubmit, DedupePolicy,
    applied_receipt,
)
from lazily.ipc import IpcValue

class Transport:
    def __init__(self):
        self.sent = []

    def send(self, message):
        self.sent.append(message)

client = CommandRpcClient(Transport())
cmd_id = client.submit(CommandSubmit(
    command_id="cmd-1", causation_id="cmd-1", source="plugin",
    target="controller", namespace="agent-doc", name="editor_route",
    authority_generation=1, idempotency_key="doc:run", deadline_ms=0,
    policy=CommandPolicy(DedupePolicy.SAME_IDEMPOTENCY_KEY, False, True),
    payload_type="agent-doc.editor_route.v1", payload_hash="sha256:…",
    payload=IpcValue.of(b"{…}"),
    required_features=["command-plane-v1"],
))
# `call` resolves ONLY on a terminal receipt — never an ACK or `accepted`.
client.ingest_receipt(applied_receipt("rcpt-1", cmd_id, "controller", 1))
assert client.poll_call(cmd_id).kind.value == "resolved"

CommandProjection is the pure reducer (generation guards, idempotency, cancel-before-terminal-only, terminal-conflict-fails-closed, reconnect equivalence); CommandRpcClient is the derived RPC facade. The wire codec validates against lazily-spec's message-passing.json, and all eight conformance/message-passing/ fixtures replay.

Benchmarks

Wall-clock benchmarks live in BENCHMARKS.md, covering both the in-library micro-suite (reactive core, keyed reconciliation, CellMap, TextCrdt, CRDT plane) and a large spreadsheet-shaped scale suite that mirrors the lazily-rs / lazily-go scale groups (N input cells + N formula slots, formula[i] = input[i] + input[i-1]). The scale suite is measured up to a full 10,000,000-cell Google Sheets workbook (N = 5,000,000); a one-cell edit plus a 1,000-cell viewport read stays in the ~75 µs range regardless of sheet size, because the lazy pull model recomputes only the ~2 formulas that read the edited input.

make bench          # micro-suite
make bench-scale    # scale suite (default N = 1,000,000)

# or directly, with a custom size:
uv run python -m lazily.benchmarks
LAZILY_SCALE_N=5000000 uv run python -m lazily.scale_bench   # 10M-cell workbook

See BENCHMARKS.md for the full results, hardware, and honest notes on CPython's per-node overhead.

The lazily family

lazily-py is one binding in a cross-language reactive family that shares the lazily-spec wire protocol:

Binding	Language	Package
lazily-rs	Rust	lazily (crates.io)
lazily-py	Python	lazily (PyPI)
lazily-zig	Zig	GitHub
@lazily/signaling	TypeScript / Cloudflare Worker	npm
lazily-spec	—	wire protocol + conformance fixtures
lazily-formal	—	Lean 4 formal model (FSM kernel + Harel state chart)

See lazily-spec for the canonical Snapshot/Delta schemas, the IPC Lean proofs of the epoch/memo/batch invariants, and the conformance fixtures every IPC-capable binding validates against. The language-agnostic formal model — the flat FSM kernel and the full Harel state chart — lives in lazily-formal.

Development

This project uses uv. Run the local CI-equivalent suite — type-check (ty), lint (ruff), the runnable README example, and the test suite — with:

uv run poe precommit

SPEC.md is the authoritative specification for the Python primitives and the lazily-spec compliance notes.